I HAVE long been engaged upon certain problems that lie at the base of the
science of heredity, and during several years have published technical memoirs
concerning them, a list of which is given in Appendix A. This volume contains
the more important of the results, set forth in an orderly way, with more
completeness than has hitherto been possible, together with a large amount of
new matter.

The inquiry relates to the inheritance of moderately exceptional qualities by
brotherhoods and multitudes rather than by individuals, and it is carried on
by more, refined and searching methods than those usually employed in
hereditary inquiries.

One of the problems to be dealt with refers to the curious regularity commonly
observed in the statistical peculiarities of great populations during a long
series of generations. The large do not always beget the large, nor the small
the small, and yet the observed proportions between the large _and the small
in each degree of size and in every quality, hardly varies from one generation
to another.

A second problem regards the average share contributed to the personal
features of the offspring by each ancestor severally. Though one half of every
child may be said to be derived from either parent, yet he may receive a-
heritage from a distant progenitor that neither of his parents possessed as
personal characteristics. Therefore the child does not on the average receive
so much as one half of his personal qualities from each parent, but something
less than a half. The question I have to solve, in a reasonable and not merely
in a statistical way, is, how much less?

The last of the problems that I need mention now, concerns the nearness of
kinship in different degrees. We are all agreed that a brother is nearer akin.
than a nephew, and a nephew than a cousin, and so on, but how much nearer are
they in the precise language of numerical statement ?

These and many other problems are all fundamentally connected, and I have
worked them out to a first degree of approximation, with some completeness.
The conclusions cannot however be intelligibly presented in an introductory
chapter. They depend on ideas that must first be well comprehended, and which
are now novel to the large majority of readers and unfamiliar to all. But
those who care to brace themselves to a sustained effort, need not feel much
regret that the road to be travelled over is indirect, and does not admit of
being mapped beforehand in a way they can clearly understand. It is full of
interest of its own. It familiarizes us with the measurement of variability,
and with curious laws of chance that apply to a vast diversity of social
subjects. This part of the inquiry may be said to run along a road on a high
level, that affords wide views in unexpected directions, and from which easy
descents may be made to totally different goals to those we have now to reach.
I have a great subject to write upon, but feel keenly my literary incapacity
to make it easily intelligible without sacrificing accuracy and thoroughness.